Limit theorems for extremes of non-stationary processes

Passeggeri Riccardo, Imperial College London

The modeling of clusters of extremes in stationary (regularly varying) processes has been extensively studied in the last ten years. However, the literature has so far considered only specific and unrealistic index sets. In Passeggeri and Wintenberger (2024), the authors provide a general framework to study extremes of stationary regularly varying random fields over arbitrary index sets. This allows for the consideration of extremes of processes over any possible shape in any finite dimension — for example, extreme precipitations over a certain region with possible missing values. Both in the existing literature and in Passeggeri and Wintenberger (2024), the process is assumed to be stationary. In this talk, I will demonstrate how it is possible to use the general framework developed in Passeggeri and Wintenberger (2024) to study clustering of extremes beyond the stationary case. But why is this important? Apart from the practical usefulness of having results that adapt to non-stationary processes, this is crucial because, from a theoretical standpoint, it was widely believed that stationarity was an unavoidable condition. From a mathematical point of view, the main results will consist of limit theorems for empirical processes. This is a joint work with Olivier Wintenberger (Sorbonne University). References: - Passeggeri, R., and Wintenberger O. Extremes for stationary regularly varying random fields over arbitrary index sets. Accepted in Extremes, 1-68 pp, 2024.

Area: CS19 - Advances in statistics for stochastic processes (Sara Mazzonetto)

Keywords: extremes, limit theorems, non-stationarity, empirical processes